Somali Islamist rebels warned they will bring the "flames of war" to Nairobi after Kenyan forces mounted a cross-border land and air assault over the weekend.

"We say to Kenya: did you consider the consequences of the invasion?" Sheikh Ali Mohamud Rage, spokesman for the al-Shabab militants, told reporters near Mogadishu. "We know fighting more than you and defeated other invaders. Your attack [on] us means your skyscrapers will be destroyed, your tourism will disappear. We shall inflict on you the same damage you inflicted on us."

In a rare show of force, dozens of Kenyan military vehicles, including tanks, crossed into Somalia on Sunday in an attempt to drive the militants away from the border. Together with pro-government Somalia forces they pushed more than 60 miles into Somalia, towards the town of Afmadow. No clashes have yet been reported, although five Kenyan airmen died when their helicopter crashed.

The Kenyan government has come under increasing pressure to control its border with Somalia after Somali gunmen carried out a string of kidnappings on its territory in recent weeks. Two women – one British, one French – were abducted in separate incidents on the coast, causing damage to Kenya's tourist industry.

Al-Shabab militants have denied involvement, although the captives passed through territory under their control, and may still be there.

Speaking on Saturday, ahead of the incursion, Kenya's internal security minister, George Saitoti, said forces would pursue the rebels deeper into Somalia. "For the first time our country is threatened with the most serious level of terrorism," he said. Kenyan troops have made brief, low-key incursions into Somalia in recent years. However, security analysts say the latest operation is dangerous as Kenya has never before engaged in conflict outside its borders.

Given the huge territory that al-Shabab controls, it is unlikely that Kenya could defeat the rebels. A more likely intention is to send the Islamists a message and establish a buffer zone along the Kenyan border that would be controlled by friendly Somali forces, including thousands of government troops trained in Kenya. Holding territory will be difficult, however, since the al-Qaida-linked militants are skilled in guerrilla war, as was demonstrated after Ethiopia invaded Somalia in late 2006.

Roland Marchal, an expert in Africa at the Centre for International Studies and Research in Paris, said Kenya's decision could aid the rebels, who have given up most of their territory in Mogadishu in recent months.

"If I was Godane [the al-Shabab leader] I would send a letter of thanks to Kenya," he said. "Al-Shabab has been in crisis politically but this could stop the internal dissent, give them a clear enemy and generate fresh support from Somalis."

Until now, Somali rebels have focused their external threats on Burundi and Uganda, whose peacekeepers protect the government in Mogadishu.

Last July, suicide bombers recruited by al-Shabab killed 76 people in the Ugandan capital – an attack the rebel spokesman warned would be replicated in Kenyaon its soil, but senior figures maintain what Marchal called a "gentlemen's agreement" with the Islamists, allowing the rebels to filter in and out of Kenya in exchange for holding off on attacks. Both sides profit from the illicit border trade in goods, especially sugar.

The weekend's military operation may signal the end of that understanding and heighten the risk of a terror strike in Kenya, according to Richard Cornwell, an independent security analyst in South Africa.

On Monday night it emerged that two British nationals were arrested in Kenya, near the border with Somalia.

The pair are believed to be from Cardiff, and South Wales police said it was in contact with local law enforcement officials to establish the circumstances of the detention. Their families have been notified.

The force said: "These persons are being detained under Kenyan law and the force is liaising with local law enforcement to establish the circumstances of their detention.

"South Wales police is also in contact with the Foreign and Commonwealth Office and the British embassy in Nairobi."

A Foreign Office spokesman said: "We are aware of reports of two British nationals detained in Kenya on 16 October and we are seeking normal consular access."